闵可夫斯基空间中的逆黑塞曲率流 II：无穷远狄利克雷问题
Inverse Hessian Curvature Flow in Minkowski Space II: The Dirichlet problem at infinity
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中文总结 AI 辅助
本文研究闵可夫斯基空间中非紧致类空严格凸超曲面的逆σ_k曲率流，证明其存在整体解且归一化后收敛到对应唯一自收缩子，丰富了非紧致情形下自收缩子的相关理论。
中文摘要 AI 辅助
本文研究闵可夫斯基空间中非紧致类空严格凸超曲面的自收缩子及逆σ_k曲率流的长时间行为。与共紧致情形中对应自收缩子具有刚性不同，非紧致问题存在由渐近数据确定的丰富自收缩子类。更确切地，我们将自收缩子方程表述为双曲空间上的完全非线性狄利克雷问题，其理想边界上带有规定数据，并证明每个连续负边界值确定唯一的整个类空严格凸自收缩子。我们进一步研究从满足无穷远下解条件且σ_k曲率有一致正下界的整个类空严格凸超曲面出发的逆σ_k曲率流，证明该流的整体存在性，并证明归一化流局部光滑收敛到具有相同无穷远规定边界值的唯一自收缩子。
英文摘要
This paper studies self-shrinkers and the long-time behavior of the inverse $σ_k$ curvature flow for noncompact entire spacelike strictly convex hypersurfaces in Minkowski space. In contrast to the co-compact setting, where the corresponding self-shrinker is rigid, the noncompact problem admits a rich family of self-shrinkers determined by their asymptotic data. More precisely, we formulate the self-shrinker equation as a fully nonlinear Dirichlet problem on hyperbolic space with prescribed data on its ideal boundary, and prove that every continuous negative boundary value determines a unique entire spacelike strictly convex self-shrinker. We further study the inverse $σ_k$ curvature flow starting from an entire spacelike strictly convex hypersurface satisfying a subsolution condition at infinity and a uniform positive lower bound for its $σ_k$ curvature. We prove global existence of the flow and show that the normalized flow converges locally smoothly to the unique self-shrinker with the same prescribed boundary value at infinity.
